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Question Number 156880 Answers: 2 Comments: 0

𝛀 =Σ_(n=0) ^∞ Σ_(k=0) ^n (1/𝛑^n ) ∙ ((π/e))^k = ?

$$\boldsymbol{\Omega}\:=\underset{\boldsymbol{\mathrm{n}}=\mathrm{0}} {\overset{\infty} {\sum}}\:\underset{\boldsymbol{\mathrm{k}}=\mathrm{0}} {\overset{\boldsymbol{\mathrm{n}}} {\sum}}\:\frac{\mathrm{1}}{\boldsymbol{\pi}^{\boldsymbol{\mathrm{n}}} }\:\centerdot\:\left(\frac{\pi}{\mathrm{e}}\right)^{\boldsymbol{\mathrm{k}}} =\:? \\ $$

Question Number 156841 Answers: 1 Comments: 0

Question Number 156849 Answers: 0 Comments: 0

∫_0 ^1 ((ln(e+(1/(1−t))))/( (√t)))dt=?

$$\int_{\mathrm{0}} ^{\mathrm{1}} \frac{{ln}\left({e}+\frac{\mathrm{1}}{\mathrm{1}−{t}}\right)}{\:\sqrt{{t}}}{dt}=? \\ $$

Question Number 156835 Answers: 0 Comments: 0

Question Number 156834 Answers: 1 Comments: 0

Question Number 156828 Answers: 0 Comments: 0

Question Number 156824 Answers: 1 Comments: 0

If x − z = tan^(− 1) (yz) and z = z(x, y), find ((δz)/(δx)) , ((δz)/(δy))

$$\mathrm{If}\:\:\:\:\:\:\mathrm{x}\:\:\:−\:\:\:\mathrm{z}\:\:\:\:=\:\:\:\:\mathrm{tan}^{−\:\mathrm{1}} \left(\mathrm{yz}\right)\:\:\:\:\:\mathrm{and}\:\:\:\:\:\:\mathrm{z}\:\:\:=\:\:\:\mathrm{z}\left(\mathrm{x},\:\:\mathrm{y}\right),\:\:\:\:\:\:\mathrm{find}\:\:\:\:\frac{\delta\mathrm{z}}{\delta\mathrm{x}}\:,\:\:\:\frac{\delta\mathrm{z}}{\delta\mathrm{y}} \\ $$

Question Number 156820 Answers: 1 Comments: 3

∫ (dx/((x^2 −x+1)((√(x^2 +x+1)))))

$$\int\:\:\frac{{dx}}{\left({x}^{\mathrm{2}} −{x}+\mathrm{1}\right)\left(\sqrt{{x}^{\mathrm{2}} +{x}+\mathrm{1}}\right)} \\ $$

Question Number 156836 Answers: 0 Comments: 0

Question Number 156809 Answers: 2 Comments: 1

Solve in R x^2 + 4x = (√(40x^2 + 32x - 16))

$$\mathrm{Solve}\:\mathrm{in}\:\mathbb{R} \\ $$$$\mathrm{x}^{\mathrm{2}} \:+\:\mathrm{4x}\:=\:\sqrt{\mathrm{40x}^{\mathrm{2}} \:+\:\mathrm{32x}\:-\:\mathrm{16}} \\ $$

Question Number 156808 Answers: 0 Comments: 1

Find: 𝛀 =∫ ((x^7 - x^5 + x^3 - x)/(1 + x^(10) )) dx ; x∈R

$$\mathrm{Find}: \\ $$$$\boldsymbol{\Omega}\:=\int\:\frac{\mathrm{x}^{\mathrm{7}} \:-\:\mathrm{x}^{\mathrm{5}} \:+\:\mathrm{x}^{\mathrm{3}} \:-\:\mathrm{x}}{\mathrm{1}\:+\:\mathrm{x}^{\mathrm{10}} }\:\mathrm{dx}\:\:;\:\:\mathrm{x}\in\mathbb{R} \\ $$

Question Number 156805 Answers: 0 Comments: 0

Question Number 156795 Answers: 2 Comments: 0

prove Σ_(n=0) ^∞ (sinx)^(2n) =sec^2 x ???

$${prove}\:\underset{{n}=\mathrm{0}} {\overset{\infty} {\sum}}\left({sinx}\right)^{\mathrm{2}{n}} ={sec}^{\mathrm{2}} {x}\:??? \\ $$

Question Number 156793 Answers: 1 Comments: 0

∫_0 ^( (π/2)) ((sin2x)/(2−sin^2 2x))dx

$$\int_{\mathrm{0}} ^{\:\frac{\pi}{\mathrm{2}}} \frac{{sin}\mathrm{2}{x}}{\mathrm{2}−{sin}^{\mathrm{2}} \mathrm{2}{x}}{dx} \\ $$

Question Number 156789 Answers: 0 Comments: 1

Question Number 156788 Answers: 3 Comments: 0

lim_(x→1) ((x+x^2 +x^3 +.....x^n −n)/(x+x^2 +x^3 +.....x^m −m))=? (0/0)

$$\underset{{x}\rightarrow\mathrm{1}} {\mathrm{lim}}\frac{{x}+{x}^{\mathrm{2}} +{x}^{\mathrm{3}} +.....{x}^{{n}} −{n}}{{x}+{x}^{\mathrm{2}} +{x}^{\mathrm{3}} +.....{x}^{{m}} −{m}}=?\:\:\:\:\frac{\mathrm{0}}{\mathrm{0}} \\ $$

Question Number 156779 Answers: 2 Comments: 0

∫((ln(1+x^2 ))/(1+x^2 ))

$$\int\frac{{ln}\left(\mathrm{1}+{x}^{\mathrm{2}} \right)}{\mathrm{1}+{x}^{\mathrm{2}} } \\ $$

Question Number 156761 Answers: 2 Comments: 0

prove that ∫((a + b sin x)/((b + a sin x)^2 ))dx=((−cos x)/(b + a sin x))

$${prove}\:{that} \\ $$$$\int\frac{{a}\:+\:{b}\:\mathrm{sin}\:{x}}{\left({b}\:+\:{a}\:\mathrm{sin}\:{x}\right)^{\mathrm{2}} }{dx}=\frac{−\mathrm{cos}\:{x}}{{b}\:+\:{a}\:\mathrm{sin}\:{x}} \\ $$

Question Number 156807 Answers: 1 Comments: 3

f(x)=arctg(1/(x^2 +x+1)) and α=f(1)+f(2)+…+f(21) find tg(α)=?

$${f}\left({x}\right)={arctg}\frac{\mathrm{1}}{{x}^{\mathrm{2}} +{x}+\mathrm{1}}\:\:{and}\:\alpha={f}\left(\mathrm{1}\right)+{f}\left(\mathrm{2}\right)+\ldots+{f}\left(\mathrm{21}\right) \\ $$$${find}\:\:{tg}\left(\alpha\right)=? \\ $$

Question Number 156806 Answers: 1 Comments: 0

Question Number 156754 Answers: 1 Comments: 0

Question Number 156744 Answers: 2 Comments: 0

y“+y′=e^x +3x

$$\mathrm{y}``+\mathrm{y}'=\mathrm{e}^{\mathrm{x}} +\mathrm{3x} \\ $$$$ \\ $$

Question Number 156743 Answers: 2 Comments: 0

Question Number 156739 Answers: 0 Comments: 1

Question Number 156734 Answers: 1 Comments: 1

Question Number 156729 Answers: 1 Comments: 0

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